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Assume the Trump/Farage claim is true: 60% of all EU migrants are male (p = 0.60). If you randomly sample 30 migrants and calculate the proportion of males (\(\hat{p}\)), check the following conditions:

1) Random condition
2) 10% condition
3) Large counts condition

Answer :

Final answer:

The question inquires about checking the validity of using a binomial distribution in a hypothesis test concerning EU migrants' gender ratio. Conditions to be evaluated are the random condition, the 10% condition, and the large counts condition.

Explanation:

The question relates to verifying whether certain conditions are met to use a binomial distribution to model the proportion of males among EU migrants when sampling 30 individuals. The conditions that need to be checked include the random condition, the 10% condition, and the large counts condition.

Random condition: This is met if each migrant in the sample is chosen randomly. For example, every migrant has an equal chance of being selected, ensuring the sample's representativeness.

10% condition: This is satisfied if the sample size (n=30) is less than 10% of the total population of EU migrants. This rule helps ensure that the selections are independent.

Large counts condition: This requires that the expected number of successes (np) and failures (n(1-p)) are both greater than 5. For a proportion (p = 0.60), this would mean we expect at least 18 males (0.60 * 30) and 12 females (0.40 * 30), satisfying the large counts condition.

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